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Bayesian inference is used extensively to quantify the uncertainty in an inferred field given the measurement of a related field when the two are linked by a mathematical model. Despite its many applications, Bayesian inference faces challenges when inferring fields that have discrete representations of large dimension, and/or have prior distributions that are difficult to characterize mathematically. In this work we demonstrate how the approximate distribution learned by a deep generative adversarial network (GAN) may be used as a prior in a Bayesian update to address both these challenges. We demonstrate the efficacy of this approach on two distinct, and remarkably broad, classes of problems. The first class leads to supervised learning algorithms for image classification with superior out of distribution detection and accuracy, and for image inpainting with built-in variance estimation. The second class leads to unsupervised learning algorithms for image denoising and for solving physics-driven inverse problems.
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Obtaining reliable uncertainty estimates of neural network predictions is a long standing challenge. Bayesian neural networks have been proposed as a solution, but it remains open how to specify their prior. In particular, the common practice of an independent normal prior in weight space imposes relatively weak constraints on the function posterior, allowing it to generalize in unforeseen ways on inputs outside of the training distribution. We propose noise contrastive priors (NCPs) to obtain reliable uncertainty estimates. The key idea is to train the model to output high uncertainty for data points outside of the training distribution. NCPs do so using an input prior, which adds noise to the inputs of the current mini batch, and an output prior, which is a wide distribution given these inputs. NCPs are compatible with any model that can output uncertainty estimates, are easy to scale, and yield reliable uncertainty estimates throughout training. Empirically, we show that NCPs prevent overfitting outside of the training distribution and result in uncertainty estimates that are useful for active learning. We demonstrate the scalability of our method on the flight delays data set, where we significantly improve upon previously published results.
Deep neural networks have proven extremely efficient at solving a wide rangeof inverse problems, but most often the uncertainty on the solution they provideis hard to quantify. In this work, we propose a generic Bayesian framework forsolving inverse problems, in which we limit the use of deep neural networks tolearning a prior distribution on the signals to recover. We adopt recent denoisingscore matching techniques to learn this prior from data, and subsequently use it aspart of an annealed Hamiltonian Monte-Carlo scheme to sample the full posteriorof image inverse problems. We apply this framework to Magnetic ResonanceImage (MRI) reconstruction and illustrate how this approach not only yields highquality reconstructions but can also be used to assess the uncertainty on particularfeatures of a reconstructed image.
In the recent years, there has been a significant improvement in the quality of samples produced by (deep) generative models such as variational auto-encoders and generative adversarial networks. However, the representation capabilities of these methods still do not capture the full distribution for complex classes of images, such as human faces. This deficiency has been clearly observed in previous works that use pre-trained generative models to solve imaging inverse problems. In this paper, we suggest to mitigate the limited representation capabilities of generators by making them image-adaptive and enforcing compliance of the restoration with the observations via back-projections. We empirically demonstrate the advantages of our proposed approach for image super-resolution and compressed sensing.
Virtual Diagnostic (VD) is a deep learning tool that can be used to predict a diagnostic output. VDs are especially useful in systems where measuring the output is invasive, limited, costly or runs the risk of damaging the output. Given a prediction, it is necessary to relay how reliable that prediction is. This is known as uncertainty quantification of a prediction. In this paper, we use ensemble methods and quantile regression neural networks to explore different ways of creating and analyzing predictions uncertainty on experimental data from the Linac Coherent Light Source at SLAC. We aim to accurately and confidently predict the current profile or longitudinal phase space images of the electron beam. The ability to make informed decisions under uncertainty is crucial for reliable deployment of deep learning tools on safety-critical systems as particle accelerators.
In recent years, deep learning based methods have shown success in essential medical image analysis tasks such as segmentation. Post-processing and refining the results of segmentation is a common practice to decrease the misclassifications originating from the segmentation network. In addition to widely used methods like Conditional Random Fields (CRFs) which focus on the structure of the segmented volume/area, a graph-based recent approach makes use of certain and uncertain points in a graph and refines the segmentation according to a small graph convolutional network (GCN). However, there are two drawbacks of the approach: most of the edges in the graph are assigned randomly and the GCN is trained independently from the segmentation network. To address these issues, we define a new neighbor-selection mechanism according to feature distances and combine the two networks in the training procedure. According to the experimental results on pancreas segmentation from Computed Tomography (CT) images, we demonstrate improvement in the quantitative measures. Also, examining the dynamic neighbors created by our method, edges between semantically similar image parts are observed. The proposed method also shows qualitative enhancements in the segmentation maps, as demonstrated in the visual results.
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